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The spelling Hangeul/hangeul is from the Korean spelling in the 1959-SK transcription and the 2000 South Korean Revised transcription. Hangul derives from the older McCune-Reischauer transcription hangŭl written without the diacritics: it is the more common English spelling. Within the English Wiktionary, hangeul is preferred.
한글 (han'geul) is the official name in South Korea, and 조선글 (朝鮮글, joseon'geul) is the official name in North Korea; hence, scholars may prefer to use Hangeul in reference to South Korea, and Chosongul in reference to North Korea.